Increasingly wind power turbines are and will be connected to an electrical grid via a series-compensated transmission line having a capacitor connected in series with the transmission line. The capacitor compensates the voltage drop across the primarily-inductive transmission line. Use of series capacitors allows the transfer of more power on a series compensated transmission line than on a line without series compensation. Line compensation is a cost effective solution for increasing the capacity of a transmission system because, typically, installation of series capacitors is less expensive than construction of new transmission lines.
Disadvantageously, series-compensated transmission lines are prone to exhibit subsynchronous oscillations (SSOs). These subsynchronous oscillations occur when the electric power system exchanges energy with the physical components of the turbine-generators (including high and low pressure turbines, the generator and the exciter, all of which share a common shaft) at one or more frequencies below the electrical system synchronous frequency. Thus these oscillations are referred to as subsynchronous oscillations.
Subsynchronous torsional interactions (SSTI) are produced when a disturbance-caused electrical resonant frequency excites a natural torsional mode (mechanical) frequency of the turbine-generator shaft (e.g., of a synchronous or an induction generator). The series compensated line with its lower electrical resonant frequency interacts with the torsional natural frequency of the turbine-generator shaft, exciting the subsynchronous oscillations in the generator. Even small magnitude disturbances in the electrical power system can create large magnitude subsynchronous resonance oscillations in the turbine-generator shaft, which are typically lightly damped. Such an excitation of a resonance by SSOs is commonly called subsynchronous resonance (SSR). When it involves a torsional natural frequency of a turbine-generator shaft, the SSR is commonly called an SSTI.
When a mechanical torsional oscillation mode is excited by the SSOs, the rotor of the synchronous generator acts like an induction generator rotor operating at the “slip” frequency, where the slip frequency is the difference between the system frequency and the SSR frequency. This action amplifies the SSR currents and causes the turbine-generator shaft to oscillate at its natural torsional frequency. Within seconds, these undamped resonant oscillations may increase to an endurance limit of the shaft, resulting in shaft fatigue and possibly damage and failure.
At a New Mexico plant in 1970, connected to a roughly 90% series compensated transmission line, the SSR oscillations were sufficiently intense to physically break the generator shaft, causing significant damage to the turbine and generator.
SSR oscillations can also interact with a wind turbine control system and thereby potentially excite torsional oscillations in the wind turbine generator shaft. These types of SSRs are commonly called subsynchronous control interactions (SSCI).
Induction generators (DFIGs and directly-connected wind turbines) have torsional natural frequencies that can respond to subsynchronous excitation, resulting in SSTI. This type of machine can also go into a “self-excitation mode” when the series capacitor resonates with the electrical inductances of the machine and of the transmission line and interconnecting transformers.
SSCI on a series compensated line has been identified as causing damage to doubly-fed induction generator (DFIG) wind turbines in Texas.
FIG. 1 illustrates a transmission line 1 with a source generator 2 and a load or receiving end generator 3. FIG. 2 is a vector diagram illustrating the relationship among the source voltage VS, the load end or receiving end voltage VR and the line inductive reactance jXLl, where XL is the inductive reactance per unit length of line and l is the line length. This analysis ignores the line resistance. The maximum power that can be carried by the line is responsive to the variable δ1, the angle between the source voltage and the receiving end voltage. As the line impedance declines (or is compensated by a series capacitor) the length of the vector jXLl becomes shorter, the length of the vectors VS and VR approach equality, the angle δ1 approaches 0, and the power transfer capacity of the transmission line approaches its maximum.
FIG. 3 illustrates a series compensated line 5 with a capacitor C in series with the line inductance L. FIG. 4 is a vector diagram illustrating the relationship among the source voltage VS, the load end or receiving end voltage VR, the inductive line reactance jXLl and the compensating series capacitive reactance −jXCl, where XC is the capacitive reactance per unit line length and l is the line length. The series capacitor compensates or cancels a portion of the inductive reactance as shown by the vector diagram, resulting in an angle δ2 less than the angle δ1.
Thus the transmission line in the series compensated case of FIG. 3 can carry more power than the uncompensated line of FIG. 1.
The power transfer capacity of a transmission line can also be expressed as proportional to the quantity V2/XL, where V is the voltage and XL is the inductive reactance of the line. If a series capacitor is introduced into the line, the power transfer capacity is V2/(XL−XC), where XC is the reactance of the series capacitor. If the series capacitive reactance is half of the series inductive reactance, the power transfer capacity doubles.
In the cases presented above, an increase in power transfer capability comes at the expense of creating an electrical resonant subsynchronous frequency equal to 60×(√/(XC/XL)) in a 60 Hz system. For example, a line that has 70% ratio series compensation (i.e., XC/XL=0.7) has a resonant frequency of roughly 50 Hz (i.e., 60×√(0.7)=50.2). To a generator rotor operating at 60 Hz, this appears to be a pair of frequencies of roughly 10 Hz and 70 Hz. The former value is determined as the difference between the system electrical frequency (60 Hz) and the mechanical resonant frequency (50 Hz). The supersynchronous frequency of 70 Hz is usually damped by mechanical system components, but the low frequency (or subsynchronous frequency) of 10 Hz is only lightly damped and may grow if excited by continual subsynchronous oscillations produced within the transmission system. If a generator rotor torsional natural frequency is at or near this subsynchronous frequency the torsional mode is excited, generating additional SSR currents at the subsynchronous frequency and creating a positive feedback situation (i.e., more SSR current creating larger oscillations, etc.). These oscillations can impose high magnitude excitations on the generator shaft, ultimately causing damage to the rotor shaft. For example, these excitations can cause torsional fatigue, due to excessive shaft twisting, that can eventually lead to shaft failure and/or damage to components attached to the shaft.
In addition to increasing power transfer capacity, series capacitors also improve transient and steady state system stability, reduce rapid voltage fluctuations, and reduce line losses. However, as described, the use of series capacitors may promote SSR in the power system as a series compensated transmission line inevitably has a lower electrical resonant frequency than the fundamental frequency (e.g., 50 Hz or 60 Hz) of the power system.
The causes and consequences of subsynchronous resonance are exacerbated by the continued growth of power transmission system interconnections. Also, transmission line inductance changes with time as generators and loads are brought on and off line, as transformers outages occur and as transmission systems topologies are changed to accommodate power demands.
Interactions between a series compensated line and power electronic device (such as a static VAR compensator) and the torsional natural frequency of a generator are referred to as subsynchronous torsional interactions (SSTI). Interactions between a power electronic controller and a series-compensated transmission system are referred to as subsynchronous control instability (SSCI). Both SSTI and SSCI are considered subcategories of SSR and are types of Subsynchronous Interactions (SSI).
SSOs distort the voltages and currents on the transmission system, and are typically expensive and difficult to filter out. These distorted voltages and currents are processed by the control elements of the transmission system (static VAR compensators, for example), possibly causing improper firing of thyristors or insulated gate bipolar transistors that comprise these control elements. As a result, a compensator itself can introduce negative damping and other instabilities into the system, resulting in SSCI.
Actual and potential damage resulting from the effects of these SSOs have discouraged electric utilities from using series capacitor compensation with synchronous generators. In fact, for several years after the New Mexico incident the utility industry throughout the world largely stopped installing new series capacitors to compensate series inductive reactance. Instead, utilities installed new transmission lines (because of the inability to extend the capability of existing lines by using series capacitor compensation) or found ways to exercise existing lines to higher capability.
Utilities began using FACTS (Flexible AC Transmission System) controllers, including static synchronous compensators (STATCOMS) to control SSOs. As a result of these efforts to reduce SSOs, the use of series capacitor compensation appears to be staging a comeback, in particular in Texas and the western US.
FACTS controllers control both real and reactive power flow on a transmission line. Since STATCOMS (one class of FACTS controllers) were developed in the early 1990s by Westinghouse Electric Corporation, several schemes have been developed using STATCOMs to damp SSR oscillations. One technique is described in a paper entitled, “A Novel Approach for Subsynchronous Resonance Damping Using a STATCOM” by Rai, et al., which was presented at the Fifteenth National Power Systems Conference in Bombay, India in December 2008.
The SSR oscillations are a 3-phase balanced voltage set. Therefore, another technique employs a shunt-connected STATCOM controller to deliberately introduce a phase voltage imbalance (by introducing an asymmetrical voltage) to reduce the electromechanical coupling between the electrical and mechanical components of the turbine-generator. The reduced coupling reduces the exchange of energy between the electrical and mechanical components and limits the effects of the SSR oscillations.
Other FACTS-based devices and techniques to damp SSR oscillations include: thyristor-controlled series compensators, the NGH series damper and solid state series compensators (SSSC). These devices are expensive and difficult to operate and control. Further, they must be protected from the effects of short circuits and the attendant short circuit current they are subjected to.
Due to current efforts to reduce consumption of natural resources, the conversion of wind energy to electrical energy using wind turbine generators is becoming more prevalent. Wind turbines exploit wind energy by converting the wind energy to electricity for distribution to end users.
A fixed-speed wind turbine is typically connected to the grid through an induction (asynchronous) generator for generating real power. Wind-driven blades drive a rotor of a fixed-speed wind turbine that in turn operates through a gear box (i.e., a transmission) at a fixed rotational speed. The fixed-speed gear box output is connected to the induction generator for generating real power. The rotor and its conductors rotate faster than the rotating flux applied to the stator from the grid (i.e., higher than the synchronous field frequency). At this higher speed, the direction of the rotor current is reversed, in turn reversing the counter EMF generated in the rotor windings, and by generator action (induction) causing current (and real power) to be generated in and flow from the stator windings. The frequency of the generated stator voltage is the same as the frequency of the applied stator voltage providing the excitation. The induction generator may use a capacitor bank for reducing reactive power consumption (i.e., the power required to generate the stator flux) from the power system.
The fixed-speed wind turbine is simple, reliable, low-cost and proven. But its disadvantages include uncontrollable reactive power consumption (as required to generate the stator rotating flux), mechanical stresses, limited power quality control and relatively inefficient operation. In fact, wind speed fluctuations result in mechanical torque fluctuations that then result in fluctuations in the electrical power on the grid.
In contrast to a fixed-speed wind turbine, the rotational speed of a variable speed wind turbine can continuously adapt to the wind speed, with the blade speed maintained at a relatively constant value corresponding to a maximum electrical power output through the use of a gear box disposed between the wind turbine rotor and the generator rotor. The variable speed wind turbine may be of a doubly-fed induction generator (DFIG) design or a full converter design. The doubly-fed induction generator uses a partial converter to provide power from the wound induction generator rotor and the power system
The full converter wind turbine is typically equipped with a synchronous or asynchronous generator (the output of which is a variable frequency AC based on the wind speed) and connected to the grid through a power converter that rectifies the incoming variable AC to DC and inverts the DC to a fixed-frequency 60 Hz AC. Variable-speed wind turbines have become widespread due to their increased efficiency over fixed-speed wind turbines and superior ancillary service capabilities.
The present invention controls a variable speed wind turbine systems to avoid exciting SSOs on an electrical transmission system and a method related thereto. Further, the present invention isolates a variable speed wind turbine from the effects of SSR on the electrical transmission system.